Question
Let 
be three vectors of magnitude 5, 3, 1 respectively. If each one is perpendicular to the sum of other two vectors, prove that 
Solution
We have
...(1)
Since
is perpendicular to 
, 
is perpendicular to 
is perpendicular to 
...(2)
...(3)
and
...(4)
Now,
...(1)Since
is perpendicular to , is perpendicular to is perpendicular to ...(2) ...(3)and
...(4)Now,
